POVM - Neumark's Dilation Theorem

Neumark's Dilation Theorem

Note: An alternate spelling of this is "Naimark's Theorem"

Neumark's dilation theorem is the classification result for POVM's. It states that a POVM can be "lifted" by an operator map of the form V*(·)V to a projection-valued measure. In the physical context, this means that measuring a POVM consisting of a set of n > N rank-one operators acting on a N-dimensional Hilbert space can always be achieved by performing a projective measurement on a Hilbert space of dimension n.